3 edition of **Spectral methods for time dependent problems** found in the catalog.

Spectral methods for time dependent problems

Eitan Tadmor

- 369 Want to read
- 25 Currently reading

Published
**1990**
by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va
.

Written in English

- Chebyshev approximations.,
- Fourier analysis.,
- Hyperbolic differential equations.,
- Parabolic differential equations.,
- Spectral methods.

**Edition Notes**

Statement | Eitan Tadmor. |

Series | ICASE interim report -- no. 14., NASA contractor report -- 187443., NASA contractor report -- NASA CR-187443. |

Contributions | Institute for Computer Applications in Science and Engineering. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15406043M |

Spectral methods book/resource suggestion. In the past months, I've been trying to learn spectral methods. My professor suggested this book: Spectral methods for time-dependent problems, David Gottlieb, Jan S Hesthaven, and Sigal Gottlieb. But, honestly, I can't understand any of this. In particular, I'm focusing on implementing Fourier-Galerking/Collocation/Tau methods. When applying spectral methods to time-dependent PDEs, the solution is typically written as a sum of basis functions with time-dependent coefficients; substituting this in the PDE yields a system of ODEs in the coefficients which can be solved using any numerical method for ODEs.

This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other book consists of three parts. Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more/5(1).

Abstract. Krylov subspace spectral (KSS) methods have previously been applied to the variable-coefficient heat equation and wave equation, as well as systems of coupled equations such as Maxwell’s equations, and have demonstrated high-order accuracy, as well as stability characteristic of implicit time-stepping schemes, even though KSS methods are explicit. SPECTRAL METHODS FOR TIME DEPENDENT PROBLEMS Eitan Tadmor' School of Mathematical Sciences, Tel-Aviv University TABSTRACT This short review on spectral approximations for time-dependent problems consists of three parts. In part I we discuss some basic ingredients from the spectral Fourier and Cheby-shev approximation theory.

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Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners.

This class-tested introduction, the first on the subject, is ideal for graduate courses, or by: Spectral methods for time-dependent problems. Jan S. Hesthaven, Professor Sigal Gottlieb, David Gottlieb. Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners.

This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. Book description. Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners.

This class-tested introduction, the first on the subject, is ideal for graduate courses, or by: This book is distinguished by the exclusive treatment of time-dependent problems, and so the derivation of spectral methods is influenced primarily by the research on finite-difference schemes, and less so by the finite-element methodology.

DOI: /CBO Corpus ID: Spectral Methods for Time-Dependent Problems @inproceedings{HesthavenSpectralMF, title={Spectral Methods for Time-Dependent Problems}, author={J. Hesthaven and S. Gottlieb and D. Gottlieb}, year={} }.

Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study.

Spectral Methods for Time-Dependent Problems (Cambridge Monographs on Applied and Computational Mathematics)5/5. DOWNLOAD NOW». Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners.

This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential.

Spectral Methods for Time dependent Problems. Tuesday & Thursday 2– IPAM Building Room # Instructor: Professor Eitan Tadmor e-mail: [email protected], Oﬃce: MS During the last three decades, spectral methods have emerged as successful, and of- ten superior, alternatives to the better known ﬁnite diﬀerence and ﬁnite element methods.

Applications include several key. Spectral Methods for Time-Dependent Problems. Both the derivative operator in Hilbert space and the matrix D M are non-normal, and we recall the illuminating book [62], where the fundamental. The theory of spectral methods for time dependent partial differential equations is reviewed.

When the domain is periodic Fourier methods are presented while for nonperiodic problems both. Spectral methods are useful techniques for solving integral and partial differential equations, many of which appear in fluid mechanics and engineering problems.

Based on a graduate course, this book presents these popular and efficient techniques with both rigorous analysis and extensive coverage of their wide range of applications. This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems.

Spectral Methods for Time-Dependent Problems. Cambridge Monographs on Applied and Computational Mathemat Cambridge University Press, Cambrigde, UK, pages. Where to find it. This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows.

Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains.

The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. Get this from a library. Spectral Methods for Time-Dependent Problems. [Jan Hesthaven; Sigal Gottlieb; David Gottlieb] -- Spectral methods are useful techniques for solving integral and partial differential equations, many of which appear in fluid mechanics and engineering problems.

Based on a graduate course, these. excellent books on spectral methods by authors who are well-known and active researchers in this ﬁeld. This book is distinguished by the exclusive treatment of time-dependent problems, and so the derivation of spectral methods is inﬂu-enced primarily by the research on ﬁnite-difference schemes, and less so by the ﬁnite-element methodology.

These problems include steady-state problems involving Helmholtz and Stokes equations, as well as time-dependent problems like the Allen-Cahn equation. Every chapter ends with a set of problems for practice. MATLAB code for applying spectral methods to various types of problems is available online.

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and .The goal of this book is to teach spectral methods for solving boundary value, eigenvalue, and time-dependent problems.

Although the title speaks only of Chebyshev polynomials and trigonometric functions, the book also discusses Hermite, Laguerre, rational Chebyshev, sinc. Spectral Methods Computational Fluid Dynamics SG Philipp Schlatter problems in simple geometries) spectral methods are very adapted and eﬃcient discreti-sation schemes.

In fact, spectral methods were among the ﬁrst to be used in practical ﬂow simulations. are the corresponding time-dependent coeﬃcients. Note that usually the.